 
Name  hadamard_4 
Classification  ncbd4 
Problem type  hadamard 
Description  Maximize determinant of 4 times 4 binary matrix 
 
Objective sense  max 
Variables  16 (16 binary, 0 general integer, 0 continuous) 
Nonlinear variables  16 
Constraints  0 
Nonlinear constraints  0 
Linear nonzeros  0 
Nonlinear nonzeros  24 
 
Download  hadamard_4.pip.gz 
Best known solution  
Best known objective  3 
Best known bound  3 
 
Originator  Marc Pfetsch 
Formulator  Marc Pfetsch 
Donator  Marc Pfetsch 
 
References 

Links 

 
Additional information  Let a(n) be the maximal determinant of a 0/1matrix of size
n by n. Hadamard proved that a(n) ≤
2^{(n)} (n+1)^{((n+1)/2)}. A Hadamard matrix
attains this bound. The Hadamard conjecture states that this is the
case if and only if n+1 is 1 or 2 or a multiple of 4. The
values of a(n) for small n are known. See the online encyclopedia of integer
sequences for more information.

 